BTW, wont Mr White be successfully saving a baddie only if the baddies tried to kill one of their own?

There's a very narrow chance for Mr White to become bad, but there's a kill role in Mr Green. So if Mr Green tries to kill a baddie and Mr White saves the baddie, Mr White becomes bad. If Mr Green is bad from the beginning, Mr White will almost certainly never be bad--a good balance in case the baddies end up with Mr Green.

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It seems like it would be very difficult to identify an undercover. The only real ways I can see doing it are: 1) an undercover targets Mr Brown and gets outed, or 2) an undercover carries out an action that is blatently something that only an undercover player would do and therefore gets their role outed by the boss or Mr Black. The undercovers can easily avoid either of these by simply not acting and just doing night kills. If the undercovers have abilities like spying or redirecting or blocking then they probably aren't all that useful anyway so they're not missing out on much by not acting.

Proposal 1:

Because of that, it seems to me like it would be useful to demand that people who can act at night do actually act (and therefore put themselves at risk of being detected by Mr Brown) and post some sort of evidence that they acted, or else get outed by the Boss and lynched. In fact, I might even go so far as to say that it might be all right to simply out all the roles that can act at night to force them to be accountable, mainly because no one except Mr Brown can identify factions and I honestly think that most of the night actions are sort of worthless if you not only don't know who the baddies are but also are working against baddies who can go undetected by simply not acting. The only drawback is that outing the roles that can act at night would help the undercovers identify Mr Brown by process of elimination and night kill him. I'll leave this open to discussion.

Proposal 2:

Taking proposal 1 to an extreme, the Boss might even consider just outing Mr Brown outright and demanding the doctor (who we know is not undercover) save him at night. Then everyone who can act on Mr Brown must do it and prove they did or else get lynched

Proposal 3:

I think we need Mr Green to kill every night (unless we identify the undercovers with proposal 2). Honestly, I'm pessimistic about us identifying the undercovers otherwise, so I think it makes sense to have Mr Green kill even if it's somewhat randomly because a blind lynch plus a blind Mr Green kill against a targeted undercover kill every day/night gives better odds for the mobsters than just a blind lynch against a targeted undercover kill every day/night. The argument against allowing Mr Green to kill is that, if he's undercover then the undercovers get two kills per night against one lynch a day, then the mobsters will die quickly and painfully.

The best way I can think of to allow Mr Green to kill without running the risk of an undercover Mr Green going on a rampage is that we vote every day on BOTH a person to lynch AND a person for Green to kill. If Mr Green disobeys orders, then he gets outed by the Boss and lynched the next day, and the person who he refused to kill was probably the other undercover.

Proposal 4:

Taking this one step further: if the Boss gets killed then there's nothing to stop Mr Green if he's undercover. Because of this, I think I would even go so far as to propose that Mr Green gets outed right away, in case the Boss dies early. We know that Dr White is a mobster, so he should save Mr Green from night kills because he would be a huge target (probably the most important target in the game). Unfortunately this would keep the doctor tied up, but would be the most reliable way I can imagine of giving the mobsters two daily kills against the undercover's night kill.

To break it down, here are my proposals:

1. The Boss outs everyone who can act at night in a way that can be proven, and insist that they post proof that they acted (to force the undercovers to run the risk of acting on Mr Brown)

2. Proposal #1, plus out Mr Brown, demand the doctor save him, and demand that everyone who can must act on him and post proof.

3. We vote on who Mr Green should kill every night. If Mr Green disobeys orders, then he and the person he didn't kill get lynched.

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Well, I have not checked the post for coherency of logic, but prima facie it will be like boss showing his hand to baddies undercovers (unless he is an undercover himself). What more would undercovers ask for on Night 1? Yeah, recruiting Mr White perhaps.

On a serious note though, it will be like removing a layer of protection around information. So, we will have all knowing majority v/s somewhat informed minority. We won't have to wait for information to reveal itself over the course of the game.